66 



MECHANISM OF DISINFECTION AND HEMOLYSIS 



variation curve in which all classes are equal in respect to number of 

 individuals. This equation is y = yti, where jn is the number of indi- 

 viduals in any one of the equal classes which is arbitrarily selected as 

 the mode, and y is the number of individuals having x units of resist- 

 ance less or more than the mode. It is obvious that in this par- 

 ticular case any class may be the mode. When the equation assumes 

 a different form so that the classes are unequal (as in the ordinary 

 curves found in biological work) and in consequence y varies, y^ is 

 the maximum ordinate of the variation curve. 



Fig. 2. The relation between the time curve (a) of a reaction proceeding at a 

 constant rate, and the curve of the differential equation {b) . The ordinates repre- 

 sent the extent to which the reaction has proceeded (a) or the rate at which it is 

 proceeding {h), and the abscissa; represent time. 



In order to understand the effect of changes in the shape of such 

 variation curves, that is of changes in the relative number of cells 

 having different degrees of resistance, let us retain the assumption 

 that the fundamental reaction proceeds at a uniform rate; for this 

 allows us to think of the variation curve (abscissae = resistance) as 

 being at the same time the differential of the time curve (abscissae = 

 time). Now suppose the variation curve to have the form (a, Fig. 3) 

 commonly found in biological statistics, of a "skew frequency curve of 

 limited range" whose equation according to Pearson' is 



ar\*^. 



-(-^'('-^ 



Xi) 



(1) 



where ^ is a constant, and X\ and Xi the number of degrees of resist- 

 3 Pearson, K., Phil. Tr., A, 1895, clxxxvi, 343. 



